\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  70.0 & -7.00 x_{1} & +  2.00 x_{2} & +  4.00 x_{3} & +  2.00 x_{4} & -8.00 x_{5} & +  5.00 x_{6} & -8.00 x_{7} & -5.00 x_{8} & -3.00 x_{9}\\
 x_{11}   &  -15.0 & +  7.00 x_{1} & -9.00 x_{2} & -8.00 x_{3} & +  5.00 x_{4} & +  5.00 x_{5} & -2.00 x_{6} & -2.00 x_{7} & -3.00 x_{8} & -2.00 x_{9}\\
 x_{12}   &  20.0  &   & +  3.00 x_{2} & -9.00 x_{3} & +  7.00 x_{4} & -5.00 x_{5} & +  7.00 x_{6} & +  2.00 x_{7} & -10.00 x_{8} & +  9.00 x_{9}\\
 x_{13}   &  -11.0 & -6.00 x_{1} & -9.00 x_{2} & + 10.00 x_{3} & -10.00 x_{4} & +  5.00 x_{5} & -6.00 x_{6} & +  9.00 x_{7} & + 10.00 x_{8} & +  5.00 x_{9}\\
 x_{14}   &  -1.0 & +  1.00 x_{1} & -5.00 x_{2} & +  1.00 x_{3} & +  6.00 x_{4} & +  5.00 x_{5} & -2.00 x_{6} & -5.00 x_{7} & +  3.00 x_{8} & -4.00 x_{9}\\
 x_{15}   &  15.0 & -6.00 x_{1} & -5.00 x_{2} & -7.00 x_{3} & -10.00 x_{4} &   & +  7.00 x_{6} & -10.00 x_{7} & +  6.00 x_{8} & -6.00 x_{9}\\
 x_{16}   &  -4.0  &   & + 10.00 x_{2} & -9.00 x_{3} & + 10.00 x_{4} & -2.00 x_{5} & -3.00 x_{6} & +  6.00 x_{7} & +  1.00 x_{8} & + 10.00 x_{9}\\
 x_{17}   &  1.0  &   & +  5.00 x_{2} & -1.00 x_{3} & -3.00 x_{4} & -8.00 x_{5} & +  2.00 x_{6} & -3.00 x_{7} & +  9.00 x_{8} & +  2.00 x_{9}\\
 x_{18}   &  -9.0 & +  2.00 x_{1} & -5.00 x_{2} &   & + 10.00 x_{4} & -8.00 x_{5} & -1.00 x_{6} & + 10.00 x_{7} & +  6.00 x_{8} & -5.00 x_{9}\\
\hline
z    &  0.0  &   & -1.00 x_{2} & +  4.00 x_{3} & +  3.00 x_{4} & -5.00 x_{5} &   & +  4.00 x_{7} & +  2.00 x_{8} & -3.00 x_{9}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{9}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,18$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & +  7.00 y_{10} & -7.00 y_{11} &   & +  6.00 y_{13} & -1.00 y_{14} & +  6.00 y_{15} &    &   & -2.00 y_{18}\\
 y_{2}   &  1.0 & -2.00 y_{10} & +  9.00 y_{11} & -3.00 y_{12} & +  9.00 y_{13} & +  5.00 y_{14} & +  5.00 y_{15} & -10.00 y_{16} & -5.00 y_{17} & +  5.00 y_{18}\\
 y_{3}   &  1.0 & -4.00 y_{10} & +  8.00 y_{11} & +  9.00 y_{12} & -10.00 y_{13} & -1.00 y_{14} & +  7.00 y_{15} & +  9.00 y_{16} & +  1.00 y_{17} &   \\
 y_{4}   &  1.0 & -2.00 y_{10} & -5.00 y_{11} & -7.00 y_{12} & + 10.00 y_{13} & -6.00 y_{14} & + 10.00 y_{15} & -10.00 y_{16} & +  3.00 y_{17} & -10.00 y_{18}\\
 y_{5}   &  1.0 & +  8.00 y_{10} & -5.00 y_{11} & +  5.00 y_{12} & -5.00 y_{13} & -5.00 y_{14} &   & +  2.00 y_{16} & +  8.00 y_{17} & +  8.00 y_{18}\\
 y_{6}   &  1.0 & -5.00 y_{10} & +  2.00 y_{11} & -7.00 y_{12} & +  6.00 y_{13} & +  2.00 y_{14} & -7.00 y_{15} & +  3.00 y_{16} & -2.00 y_{17} & +  1.00 y_{18}\\
 y_{7}   &  1.0 & +  8.00 y_{10} & +  2.00 y_{11} & -2.00 y_{12} & -9.00 y_{13} & +  5.00 y_{14} & + 10.00 y_{15} & -6.00 y_{16} & +  3.00 y_{17} & -10.00 y_{18}\\
 y_{8}   &  1.0 & +  5.00 y_{10} & +  3.00 y_{11} & + 10.00 y_{12} & -10.00 y_{13} & -3.00 y_{14} & -6.00 y_{15} & -1.00 y_{16} & -9.00 y_{17} & -6.00 y_{18}\\
 y_{9}   &  1.0 & +  3.00 y_{10} & +  2.00 y_{11} & -9.00 y_{12} & -5.00 y_{13} & +  4.00 y_{14} & +  6.00 y_{15} & -10.00 y_{16} & -2.00 y_{17} & +  5.00 y_{18}\\
\hline
z    &  -0 & -70.00 y_{10} & + 15.00 y_{11} & -20.00 y_{12} & + 11.00 y_{13} & +  1.00 y_{14} & -15.00 y_{15} & +  4.00 y_{16} & -1.00 y_{17} & +  9.00 y_{18}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 8 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{11}   &  0.230783217905 & +  1.54 y_{10} & -0.01 y_{9} & +  0.67 y_{12} & -0.06 y_{5} & -0.52 y_{14} & +  0.48 y_{15} & -0.05 y_{8} & -0.12 y_{1} & +  0.00 y_{7}\\
 y_{2}   &  2.9549536059 & + 15.64 y_{10} & +  1.04 y_{9} & + 20.45 y_{12} & -1.22 y_{5} & -6.82 y_{14} & +  0.29 y_{15} & -0.87 y_{8} & -0.58 y_{1} & -0.32 y_{7}\\
 y_{3}   &  2.62901837046 & +  4.52 y_{10} & -0.83 y_{9} & -4.28 y_{12} & +  0.37 y_{5} & +  4.09 y_{14} & + 23.80 y_{15} & +  0.38 y_{8} & -1.49 y_{1} & -0.05 y_{7}\\
 y_{16}   &  0.0886969543011 & +  0.37 y_{10} & -0.08 y_{9} & -1.23 y_{12} & +  0.03 y_{5} & +  0.66 y_{14} & +  1.19 y_{15} & +  0.03 y_{8} & -0.04 y_{1} & -0.03 y_{7}\\
 y_{13}   &  0.106693050245 & +  0.72 y_{10} & +  0.00 y_{9} & +  0.81 y_{12} & -0.06 y_{5} & -0.37 y_{14} & -0.28 y_{15} & -0.05 y_{8} & +  0.01 y_{1} & -0.01 y_{7}\\
 y_{6}   &  2.27733240634 & +  3.63 y_{10} & -0.16 y_{9} & -5.42 y_{12} & -0.37 y_{5} & +  1.62 y_{14} & -2.47 y_{15} & -0.18 y_{8} & -0.24 y_{1} & -0.32 y_{7}\\
 y_{18}   &  0.0123378880659 & +  0.26 y_{10} & +  0.04 y_{9} & +  0.09 y_{12} & +  0.03 y_{5} & +  0.23 y_{14} & +  0.45 y_{15} & -0.00 y_{8} & -0.03 y_{1} & -0.05 y_{7}\\
 y_{4}   &  0.0568976121079 & -8.64 y_{10} & +  0.42 y_{9} & + 10.60 y_{12} & -0.77 y_{5} & -16.95 y_{14} & -13.54 y_{15} & -0.83 y_{8} & +  1.27 y_{1} & +  0.84 y_{7}\\
 y_{17}   &  0.0514105409525 & +  0.06 y_{10} & -0.02 y_{9} & +  0.51 y_{12} & +  0.02 y_{5} & -0.33 y_{14} & -0.62 y_{15} & -0.07 y_{8} & -0.04 y_{1} & +  0.05 y_{7}\\
\hline
z    &  5.04979009011 & -35.27 y_{10} & -0.07 y_{9} & -5.69 y_{12} & -1.09 y_{5} & -5.84 y_{14} & -1.40 y_{15} & -1.09 y_{8} & -2.06 y_{1} & -0.74 y_{7}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  35.2655828008 & -1.54 x_{11} & -15.64 x_{2} & -4.52 x_{3} & -0.37 x_{16} & -0.72 x_{13} & -3.63 x_{6} & -0.26 x_{18} & +  8.64 x_{4} & -0.06 x_{17}\\
 x_{9}   &  0.0655934968046 & +  0.01 x_{11} & -1.04 x_{2} & +  0.83 x_{3} & +  0.08 x_{16} & -0.00 x_{13} & +  0.16 x_{6} & -0.04 x_{18} & -0.42 x_{4} & +  0.02 x_{17}\\
 x_{12}   &  5.68954728989 & -0.67 x_{11} & -20.45 x_{2} & +  4.28 x_{3} & +  1.23 x_{16} & -0.81 x_{13} & +  5.42 x_{6} & -0.09 x_{18} & -10.60 x_{4} & -0.51 x_{17}\\
 x_{5}   &  1.09236034976 & +  0.06 x_{11} & +  1.22 x_{2} & -0.37 x_{3} & -0.03 x_{16} & +  0.06 x_{13} & +  0.37 x_{6} & -0.03 x_{18} & +  0.77 x_{4} & -0.02 x_{17}\\
 x_{14}   &  5.83787469583 & +  0.52 x_{11} & +  6.82 x_{2} & -4.09 x_{3} & -0.66 x_{16} & +  0.37 x_{13} & -1.62 x_{6} & -0.23 x_{18} & + 16.95 x_{4} & +  0.33 x_{17}\\
 x_{15}   &  1.39901596385 & -0.48 x_{11} & -0.29 x_{2} & -23.80 x_{3} & -1.19 x_{16} & +  0.28 x_{13} & +  2.47 x_{6} & -0.45 x_{18} & + 13.54 x_{4} & +  0.62 x_{17}\\
 x_{8}   &  1.09179880739 & +  0.05 x_{11} & +  0.87 x_{2} & -0.38 x_{3} & -0.03 x_{16} & +  0.05 x_{13} & +  0.18 x_{6} & +  0.00 x_{18} & +  0.83 x_{4} & +  0.07 x_{17}\\
 x_{1}   &  2.06053961548 & +  0.12 x_{11} & +  0.58 x_{2} & +  1.49 x_{3} & +  0.04 x_{16} & -0.01 x_{13} & +  0.24 x_{6} & +  0.03 x_{18} & -1.27 x_{4} & +  0.04 x_{17}\\
 x_{7}   &  0.739497820681 & -0.00 x_{11} & +  0.32 x_{2} & +  0.05 x_{3} & +  0.03 x_{16} & +  0.01 x_{13} & +  0.32 x_{6} & +  0.05 x_{18} & -0.84 x_{4} & -0.05 x_{17}\\
\hline
z    &  -5.04979009011 & -0.23 x_{11} & -2.95 x_{2} & -2.63 x_{3} & -0.09 x_{16} & -0.11 x_{13} & -2.28 x_{6} & -0.01 x_{18} & -0.06 x_{4} & -0.05 x_{17}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  35.2655828008 & -1.54 x_{11} & -15.64 x_{2} & -4.52 x_{3} & -0.37 x_{16} & -0.72 x_{13} & -3.63 x_{6} & -0.26 x_{18} & +  8.64 x_{4} & -0.06 x_{17}\\
 x_{9}   &  0.0655934968046 & +  0.01 x_{11} & -1.04 x_{2} & +  0.83 x_{3} & +  0.08 x_{16} & -0.00 x_{13} & +  0.16 x_{6} & -0.04 x_{18} & -0.42 x_{4} & +  0.02 x_{17}\\
 x_{12}   &  5.68954728989 & -0.67 x_{11} & -20.45 x_{2} & +  4.28 x_{3} & +  1.23 x_{16} & -0.81 x_{13} & +  5.42 x_{6} & -0.09 x_{18} & -10.60 x_{4} & -0.51 x_{17}\\
 x_{5}   &  1.09236034976 & +  0.06 x_{11} & +  1.22 x_{2} & -0.37 x_{3} & -0.03 x_{16} & +  0.06 x_{13} & +  0.37 x_{6} & -0.03 x_{18} & +  0.77 x_{4} & -0.02 x_{17}\\
 x_{14}   &  5.83787469583 & +  0.52 x_{11} & +  6.82 x_{2} & -4.09 x_{3} & -0.66 x_{16} & +  0.37 x_{13} & -1.62 x_{6} & -0.23 x_{18} & + 16.95 x_{4} & +  0.33 x_{17}\\
 x_{15}   &  1.39901596385 & -0.48 x_{11} & -0.29 x_{2} & -23.80 x_{3} & -1.19 x_{16} & +  0.28 x_{13} & +  2.47 x_{6} & -0.45 x_{18} & + 13.54 x_{4} & +  0.62 x_{17}\\
 x_{8}   &  1.09179880739 & +  0.05 x_{11} & +  0.87 x_{2} & -0.38 x_{3} & -0.03 x_{16} & +  0.05 x_{13} & +  0.18 x_{6} & +  0.00 x_{18} & +  0.83 x_{4} & +  0.07 x_{17}\\
 x_{1}   &  2.06053961548 & +  0.12 x_{11} & +  0.58 x_{2} & +  1.49 x_{3} & +  0.04 x_{16} & -0.01 x_{13} & +  0.24 x_{6} & +  0.03 x_{18} & -1.27 x_{4} & +  0.04 x_{17}\\
 x_{7}   &  0.739497820681 & -0.00 x_{11} & +  0.32 x_{2} & +  0.05 x_{3} & +  0.03 x_{16} & +  0.01 x_{13} & +  0.32 x_{6} & +  0.05 x_{18} & -0.84 x_{4} & -0.05 x_{17}\\
\hline
z    &  -0.516993341712 & -0.23 x_{11} & -0.97 x_{2} & +  2.79 x_{3} & -0.05 x_{16} & -0.11 x_{13} & -0.70 x_{6} & +  0.47 x_{18} & -1.27 x_{4} & -0.04 x_{17}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  35.2655828008 & -1.54 x_{11} & -15.64 x_{2} & -4.52 x_{3} & -0.37 x_{16} & -0.72 x_{13} & -3.63 x_{6} & -0.26 x_{18} & +  8.64 x_{4} & -0.06 x_{17}\\
 x_{9}   &  0.0655934968046 & +  0.01 x_{11} & -1.04 x_{2} & +  0.83 x_{3} & +  0.08 x_{16} & -0.00 x_{13} & +  0.16 x_{6} & -0.04 x_{18} & -0.42 x_{4} & +  0.02 x_{17}\\
 x_{12}   &  5.68954728989 & -0.67 x_{11} & -20.45 x_{2} & +  4.28 x_{3} & +  1.23 x_{16} & -0.81 x_{13} & +  5.42 x_{6} & -0.09 x_{18} & -10.60 x_{4} & -0.51 x_{17}\\
 x_{5}   &  1.09236034976 & +  0.06 x_{11} & +  1.22 x_{2} & -0.37 x_{3} & -0.03 x_{16} & +  0.06 x_{13} & +  0.37 x_{6} & -0.03 x_{18} & +  0.77 x_{4} & -0.02 x_{17}\\
 x_{14}   &  5.83787469583 & +  0.52 x_{11} & +  6.82 x_{2} & -4.09 x_{3} & -0.66 x_{16} & +  0.37 x_{13} & -1.62 x_{6} & -0.23 x_{18} & + 16.95 x_{4} & +  0.33 x_{17}\\
 x_{15}   &  1.39901596385 & -0.48 x_{11} & -0.29 x_{2} & -23.80 x_{3} & -1.19 x_{16} & +  0.28 x_{13} & +  2.47 x_{6} & -0.45 x_{18} & + 13.54 x_{4} & +  0.62 x_{17}\\
 x_{8}   &  1.09179880739 & +  0.05 x_{11} & +  0.87 x_{2} & -0.38 x_{3} & -0.03 x_{16} & +  0.05 x_{13} & +  0.18 x_{6} & +  0.00 x_{18} & +  0.83 x_{4} & +  0.07 x_{17}\\
 x_{1}   &  2.06053961548 & +  0.12 x_{11} & +  0.58 x_{2} & +  1.49 x_{3} & +  0.04 x_{16} & -0.01 x_{13} & +  0.24 x_{6} & +  0.03 x_{18} & -1.27 x_{4} & +  0.04 x_{17}\\
 x_{7}   &  0.739497820681 & -0.00 x_{11} & +  0.32 x_{2} & +  0.05 x_{3} & +  0.03 x_{16} & +  0.01 x_{13} & +  0.32 x_{6} & +  0.05 x_{18} & -0.84 x_{4} & -0.05 x_{17}\\
\hline
z    &  -0.516993341712 & -0.23 x_{11} & -0.97 x_{2} & +  2.79 x_{3} & -0.05 x_{16} & -0.11 x_{13} & -0.70 x_{6} & +  0.47 x_{18} & -1.27 x_{4} & -0.04 x_{17}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{15} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  34.9996345722 & -1.45 x_{11} & -15.58 x_{2} & +  0.19 x_{15} & -0.14 x_{16} & -0.77 x_{13} & -4.09 x_{6} & -0.17 x_{18} & +  6.06 x_{4} & -0.18 x_{17}\\
 x_{9}   &  0.114558028973 & -0.01 x_{11} & -1.05 x_{2} & -0.03 x_{15} & +  0.04 x_{16} & +  0.01 x_{13} & +  0.25 x_{6} & -0.05 x_{18} & +  0.05 x_{4} & +  0.04 x_{17}\\
 x_{12}   &  5.94098745072 & -0.75 x_{11} & -20.50 x_{2} & -0.18 x_{15} & +  1.01 x_{16} & -0.76 x_{13} & +  5.86 x_{6} & -0.18 x_{18} & -8.16 x_{4} & -0.40 x_{17}\\
 x_{5}   &  1.07072039849 & +  0.06 x_{11} & +  1.22 x_{2} & +  0.02 x_{15} & -0.01 x_{16} & +  0.05 x_{13} & +  0.34 x_{6} & -0.02 x_{18} & +  0.56 x_{4} & -0.03 x_{17}\\
 x_{14}   &  5.59723155831 & +  0.61 x_{11} & +  6.87 x_{2} & +  0.17 x_{15} & -0.46 x_{16} & +  0.32 x_{13} & -2.04 x_{6} & -0.15 x_{18} & + 14.62 x_{4} & +  0.22 x_{17}\\
 x_{3}   &  0.0587909552791 & -0.02 x_{11} & -0.01 x_{2} & -0.04 x_{15} & -0.05 x_{16} & +  0.01 x_{13} & +  0.10 x_{6} & -0.02 x_{18} & +  0.57 x_{4} & +  0.03 x_{17}\\
 x_{8}   &  1.06925554081 & +  0.05 x_{11} & +  0.87 x_{2} & +  0.02 x_{15} & -0.01 x_{16} & +  0.05 x_{13} & +  0.14 x_{6} & +  0.01 x_{18} & +  0.61 x_{4} & +  0.06 x_{17}\\
 x_{1}   &  2.14840707402 & +  0.09 x_{11} & +  0.56 x_{2} & -0.06 x_{15} & -0.04 x_{16} & +  0.00 x_{13} & +  0.39 x_{6} & -0.00 x_{18} & -0.42 x_{4} & +  0.07 x_{17}\\
 x_{7}   &  0.742620593993 & -0.00 x_{11} & +  0.32 x_{2} & -0.00 x_{15} & +  0.03 x_{16} & +  0.01 x_{13} & +  0.33 x_{6} & +  0.05 x_{18} & -0.81 x_{4} & -0.05 x_{17}\\
\hline
z    &  -0.353118800678 & -0.28 x_{11} & -1.01 x_{2} & -0.12 x_{15} & -0.19 x_{16} & -0.07 x_{13} & -0.41 x_{6} & +  0.42 x_{18} & +  0.32 x_{4} & +  0.03 x_{17}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{12} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  39.4118557513 & -2.01 x_{11} & -30.81 x_{2} & +  0.06 x_{15} & +  0.61 x_{16} & -1.33 x_{13} & +  0.26 x_{6} & -0.30 x_{18} & -0.74 x_{12} & -0.47 x_{17}\\
 x_{9}   &  0.150752311086 & -0.01 x_{11} & -1.17 x_{2} & -0.04 x_{15} & +  0.04 x_{16} & +  0.00 x_{13} & +  0.28 x_{6} & -0.05 x_{18} & -0.01 x_{12} & +  0.04 x_{17}\\
 x_{4}   &  0.72784730558 & -0.09 x_{11} & -2.51 x_{2} & -0.02 x_{15} & +  0.12 x_{16} & -0.09 x_{13} & +  0.72 x_{6} & -0.02 x_{18} & -0.12 x_{12} & -0.05 x_{17}\\
 x_{5}   &  1.47511578147 & +  0.01 x_{11} & -0.17 x_{2} & +  0.00 x_{15} & +  0.06 x_{16} & -0.00 x_{13} & +  0.73 x_{6} & -0.03 x_{18} & -0.07 x_{12} & -0.06 x_{17}\\
 x_{14}   &  16.2364808183 & -0.74 x_{11} & -29.85 x_{2} & -0.15 x_{15} & +  1.36 x_{16} & -1.04 x_{13} & +  8.46 x_{6} & -0.47 x_{18} & -1.79 x_{12} & -0.49 x_{17}\\
 x_{3}   &  0.472949411668 & -0.07 x_{11} & -1.44 x_{2} & -0.05 x_{15} & +  0.02 x_{16} & -0.04 x_{13} & +  0.51 x_{6} & -0.03 x_{18} & -0.07 x_{12} & -0.00 x_{17}\\
 x_{8}   &  1.51224242196 & -0.00 x_{11} & -0.66 x_{2} & +  0.00 x_{15} & +  0.06 x_{16} & -0.01 x_{13} & +  0.58 x_{6} & -0.01 x_{18} & -0.07 x_{12} & +  0.03 x_{17}\\
 x_{1}   &  1.84426537704 & +  0.13 x_{11} & +  1.61 x_{2} & -0.05 x_{15} & -0.09 x_{16} & +  0.04 x_{13} & +  0.09 x_{6} & +  0.01 x_{18} & +  0.05 x_{12} & +  0.09 x_{17}\\
 x_{7}   &  0.151422946554 & +  0.07 x_{11} & +  2.36 x_{2} & +  0.02 x_{15} & -0.07 x_{16} & +  0.09 x_{13} & -0.25 x_{6} & +  0.07 x_{18} & +  0.10 x_{12} & -0.01 x_{17}\\
\hline
z    &  -0.12231964705 & -0.31 x_{11} & -1.80 x_{2} & -0.12 x_{15} & -0.15 x_{16} & -0.10 x_{13} & -0.18 x_{6} & +  0.41 x_{18} & -0.04 x_{12} & +  0.02 x_{17}\\
\end{array}\]


 $ x_{17} $ enters and $ x_{7} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  34.2049129484 & -4.42 x_{11} & -112.01 x_{2} & -0.48 x_{15} & +  3.13 x_{16} & -4.40 x_{13} & +  9.00 x_{6} & -2.69 x_{18} & -4.16 x_{12} & + 34.39 x_{7}\\
 x_{9}   &  0.603856646452 & +  0.20 x_{11} & +  5.90 x_{2} & +  0.01 x_{15} & -0.18 x_{16} & +  0.27 x_{13} & -0.48 x_{6} & +  0.15 x_{18} & +  0.29 x_{12} & -2.99 x_{7}\\
 x_{4}   &  0.191242449609 & -0.34 x_{11} & -10.88 x_{2} & -0.08 x_{15} & +  0.38 x_{16} & -0.41 x_{13} & +  1.62 x_{6} & -0.27 x_{18} & -0.48 x_{12} & +  3.54 x_{7}\\
 x_{5}   &  0.842716996585 & -0.28 x_{11} & -10.03 x_{2} & -0.06 x_{15} & +  0.37 x_{16} & -0.37 x_{13} & +  1.80 x_{6} & -0.32 x_{18} & -0.48 x_{12} & +  4.18 x_{7}\\
 x_{14}   &  10.826631577 & -3.24 x_{11} & -114.21 x_{2} & -0.71 x_{15} & +  3.98 x_{16} & -4.22 x_{13} & + 17.54 x_{6} & -2.95 x_{18} & -5.35 x_{12} & + 35.73 x_{7}\\
 x_{3}   &  0.456721127846 & -0.08 x_{11} & -1.69 x_{2} & -0.06 x_{15} & +  0.03 x_{16} & -0.05 x_{13} & +  0.54 x_{6} & -0.04 x_{18} & -0.08 x_{12} & +  0.11 x_{7}\\
 x_{8}   &  1.84493318318 & +  0.15 x_{11} & +  4.53 x_{2} & +  0.04 x_{15} & -0.10 x_{16} & +  0.19 x_{13} & +  0.02 x_{6} & +  0.15 x_{18} & +  0.14 x_{12} & -2.20 x_{7}\\
 x_{1}   &  2.88949780489 & +  0.62 x_{11} & + 17.91 x_{2} & +  0.05 x_{15} & -0.60 x_{16} & +  0.66 x_{13} & -1.66 x_{6} & +  0.48 x_{18} & +  0.74 x_{12} & -6.90 x_{7}\\
 x_{17}   &  11.0399274922 & +  5.11 x_{11} & + 172.17 x_{2} & +  1.14 x_{15} & -5.35 x_{16} & +  6.50 x_{13} & -18.53 x_{6} & +  5.06 x_{18} & +  7.26 x_{12} & -72.91 x_{7}\\
\hline
z    &  0.065323304286 & -0.23 x_{11} & +  1.12 x_{2} & -0.10 x_{15} & -0.24 x_{16} & +  0.01 x_{13} & -0.49 x_{6} & +  0.50 x_{18} & +  0.08 x_{12} & -1.24 x_{7}\\
\end{array}\]


 $ x_{2} $ enters and $ x_{4} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  32.2360859598 & -0.91 x_{11} & + 10.29 x_{4} & +  0.32 x_{15} & -0.82 x_{16} & -0.19 x_{13} & -7.67 x_{6} & +  0.06 x_{18} & +  0.73 x_{12} & -2.10 x_{7}\\
 x_{9}   &  0.707479093538 & +  0.01 x_{11} & -0.54 x_{4} & -0.03 x_{15} & +  0.03 x_{16} & +  0.05 x_{13} & +  0.40 x_{6} & +  0.01 x_{18} & +  0.03 x_{12} & -1.07 x_{7}\\
 x_{2}   &  0.0175772028469 & -0.03 x_{11} & -0.09 x_{4} & -0.01 x_{15} & +  0.04 x_{16} & -0.04 x_{13} & +  0.15 x_{6} & -0.02 x_{18} & -0.04 x_{12} & +  0.33 x_{7}\\
 x_{5}   &  0.66636580427 & +  0.03 x_{11} & +  0.92 x_{4} & +  0.01 x_{15} & +  0.01 x_{16} & +  0.00 x_{13} & +  0.30 x_{6} & -0.08 x_{18} & -0.05 x_{12} & +  0.91 x_{7}\\
 x_{14}   &  8.81906521709 & +  0.33 x_{11} & + 10.50 x_{4} & +  0.10 x_{15} & -0.05 x_{16} & +  0.07 x_{13} & +  0.54 x_{6} & -0.14 x_{18} & -0.36 x_{12} & -1.47 x_{7}\\
 x_{3}   &  0.426934626082 & -0.03 x_{11} & +  0.16 x_{4} & -0.04 x_{15} & -0.03 x_{16} & +  0.01 x_{13} & +  0.29 x_{6} & +  0.00 x_{18} & -0.01 x_{12} & -0.44 x_{7}\\
 x_{8}   &  1.92458027943 & +  0.01 x_{11} & -0.42 x_{4} & +  0.00 x_{15} & +  0.06 x_{16} & +  0.02 x_{13} & +  0.70 x_{6} & +  0.04 x_{18} & -0.05 x_{12} & -0.72 x_{7}\\
 x_{1}   &  3.20436311976 & +  0.06 x_{11} & -1.65 x_{4} & -0.07 x_{15} & +  0.04 x_{16} & -0.01 x_{13} & +  1.00 x_{6} & +  0.04 x_{18} & -0.04 x_{12} & -1.07 x_{7}\\
 x_{17}   &  14.0662056559 & -0.28 x_{11} & -15.82 x_{4} & -0.08 x_{15} & +  0.73 x_{16} & +  0.03 x_{13} & +  7.09 x_{6} & +  0.83 x_{18} & -0.26 x_{12} & -16.83 x_{7}\\
\hline
z    &  0.0850555583743 & -0.26 x_{11} & -0.10 x_{4} & -0.11 x_{15} & -0.20 x_{16} & -0.04 x_{13} & -0.33 x_{6} & +  0.47 x_{18} & +  0.04 x_{12} & -0.87 x_{7}\\
\end{array}\]


 $ x_{12} $ enters and $ x_{2} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  32.5287514628 & -1.43 x_{11} & +  8.76 x_{4} & +  0.20 x_{15} & -0.23 x_{16} & -0.82 x_{13} & -5.19 x_{6} & -0.35 x_{18} & -16.65 x_{2} & +  3.33 x_{7}\\
 x_{9}   &  0.721251705738 & -0.01 x_{11} & -0.61 x_{4} & -0.04 x_{15} & +  0.06 x_{16} & +  0.02 x_{13} & +  0.52 x_{6} & -0.01 x_{18} & -0.78 x_{2} & -0.82 x_{7}\\
 x_{12}   &  0.40248245677 & -0.72 x_{11} & -2.10 x_{4} & -0.16 x_{15} & +  0.81 x_{16} & -0.86 x_{13} & +  3.41 x_{6} & -0.56 x_{18} & -22.90 x_{2} & +  7.46 x_{7}\\
 x_{5}   &  0.648049649135 & +  0.07 x_{11} & +  1.02 x_{4} & +  0.02 x_{15} & -0.02 x_{16} & +  0.04 x_{13} & +  0.15 x_{6} & -0.05 x_{18} & +  1.04 x_{2} & +  0.57 x_{7}\\
 x_{14}   &  8.67494011432 & +  0.59 x_{11} & + 11.25 x_{4} & +  0.16 x_{15} & -0.34 x_{16} & +  0.38 x_{13} & -0.68 x_{6} & +  0.06 x_{18} & +  8.20 x_{2} & -4.14 x_{7}\\
 x_{3}   &  0.42437083071 & -0.02 x_{11} & +  0.17 x_{4} & -0.04 x_{15} & -0.04 x_{16} & +  0.02 x_{13} & +  0.27 x_{6} & +  0.01 x_{18} & +  0.15 x_{2} & -0.49 x_{7}\\
 x_{8}   &  1.90291971728 & +  0.05 x_{11} & -0.30 x_{4} & +  0.01 x_{15} & +  0.02 x_{16} & +  0.06 x_{13} & +  0.51 x_{6} & +  0.07 x_{18} & +  1.23 x_{2} & -1.12 x_{7}\\
 x_{1}   &  3.18656870905 & +  0.09 x_{11} & -1.55 x_{4} & -0.07 x_{15} & +  0.00 x_{16} & +  0.02 x_{13} & +  0.85 x_{6} & +  0.07 x_{18} & +  1.01 x_{2} & -1.40 x_{7}\\
 x_{17}   &  13.9600128432 & -0.09 x_{11} & -15.27 x_{4} & -0.04 x_{15} & +  0.51 x_{16} & +  0.26 x_{13} & +  6.19 x_{6} & +  0.98 x_{18} & +  6.04 x_{2} & -18.80 x_{7}\\
\hline
z    &  0.0993193945104 & -0.29 x_{11} & -0.18 x_{4} & -0.12 x_{15} & -0.17 x_{16} & -0.07 x_{13} & -0.21 x_{6} & +  0.45 x_{18} & -0.81 x_{2} & -0.61 x_{7}\\
\end{array}\]


 $ x_{18} $ enters and $ x_{12} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  32.2805900201 & -0.99 x_{11} & + 10.06 x_{4} & +  0.30 x_{15} & -0.73 x_{16} & -0.29 x_{13} & -7.29 x_{6} & +  0.62 x_{12} & -2.53 x_{2} & -1.27 x_{7}\\
 x_{9}   &  0.713431670021 & +  0.00 x_{11} & -0.57 x_{4} & -0.03 x_{15} & +  0.04 x_{16} & +  0.04 x_{13} & +  0.45 x_{6} & +  0.02 x_{12} & -0.34 x_{2} & -0.96 x_{7}\\
 x_{18}   &  0.715504551326 & -1.27 x_{11} & -3.74 x_{4} & -0.29 x_{15} & +  1.44 x_{16} & -1.53 x_{13} & +  6.06 x_{6} & -1.78 x_{12} & -40.71 x_{2} & + 13.26 x_{7}\\
 x_{5}   &  0.611379817947 & +  0.13 x_{11} & +  1.21 x_{4} & +  0.03 x_{15} & -0.10 x_{16} & +  0.12 x_{13} & -0.16 x_{6} & +  0.09 x_{12} & +  3.13 x_{2} & -0.11 x_{7}\\
 x_{14}   &  8.71910956229 & +  0.51 x_{11} & + 11.02 x_{4} & +  0.14 x_{15} & -0.25 x_{16} & +  0.28 x_{13} & -0.30 x_{6} & -0.11 x_{12} & +  5.69 x_{2} & -3.33 x_{7}\\
 x_{3}   &  0.429086430138 & -0.03 x_{11} & +  0.14 x_{4} & -0.05 x_{15} & -0.03 x_{16} & +  0.01 x_{13} & +  0.31 x_{6} & -0.01 x_{12} & -0.12 x_{2} & -0.40 x_{7}\\
 x_{8}   &  1.95022080692 & -0.04 x_{11} & -0.55 x_{4} & -0.01 x_{15} & +  0.11 x_{16} & -0.04 x_{13} & +  0.91 x_{6} & -0.12 x_{12} & -1.46 x_{2} & -0.25 x_{7}\\
 x_{1}   &  3.23618830174 & -0.00 x_{11} & -1.81 x_{4} & -0.09 x_{15} & +  0.10 x_{16} & -0.08 x_{13} & +  1.27 x_{6} & -0.12 x_{12} & -1.81 x_{2} & -0.48 x_{7}\\
 x_{17}   &  14.6587256286 & -1.34 x_{11} & -18.92 x_{4} & -0.33 x_{15} & +  1.92 x_{16} & -1.23 x_{13} & + 12.11 x_{6} & -1.74 x_{12} & -33.71 x_{2} & -5.85 x_{7}\\
\hline
z    &  0.419593234596 & -0.86 x_{11} & -1.85 x_{4} & -0.25 x_{15} & +  0.47 x_{16} & -0.75 x_{13} & +  2.50 x_{6} & -0.80 x_{12} & -19.03 x_{2} & +  5.33 x_{7}\\
\end{array}\]


 $ x_{6} $ enters and $ x_{5} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  4.80884939369 & -6.87 x_{11} & -44.29 x_{4} & -1.12 x_{15} & +  3.65 x_{16} & -5.73 x_{13} & + 44.93 x_{5} & -3.48 x_{12} & -143.10 x_{2} & +  3.69 x_{7}\\
 x_{9}   &  2.41423678608 & +  0.37 x_{11} & +  2.79 x_{4} & +  0.05 x_{15} & -0.23 x_{16} & +  0.37 x_{13} & -2.78 x_{5} & +  0.27 x_{12} & +  8.36 x_{2} & -1.27 x_{7}\\
 x_{18}   &  23.5353142646 & +  3.61 x_{11} & + 41.41 x_{4} & +  0.89 x_{15} & -2.20 x_{16} & +  2.99 x_{13} & -37.33 x_{5} & +  1.62 x_{12} & + 76.06 x_{2} & +  9.14 x_{7}\\
 x_{6}   &  3.76765713228 & +  0.81 x_{11} & +  7.45 x_{4} & +  0.19 x_{15} & -0.60 x_{16} & +  0.75 x_{13} & -6.16 x_{5} & +  0.56 x_{12} & + 19.28 x_{2} & -0.68 x_{7}\\
 x_{14}   &  7.57558085717 & +  0.26 x_{11} & +  8.76 x_{4} & +  0.09 x_{15} & -0.07 x_{16} & +  0.05 x_{13} & +  1.87 x_{5} & -0.28 x_{12} & -0.16 x_{2} & -3.12 x_{7}\\
 x_{3}   &  1.58076460243 & +  0.22 x_{11} & +  2.42 x_{4} & +  0.01 x_{15} & -0.21 x_{16} & +  0.24 x_{13} & -1.88 x_{5} & +  0.16 x_{12} & +  5.77 x_{2} & -0.61 x_{7}\\
 x_{8}   &  5.38748495788 & +  0.70 x_{11} & +  6.25 x_{4} & +  0.17 x_{15} & -0.43 x_{16} & +  0.65 x_{13} & -5.62 x_{5} & +  0.39 x_{12} & + 16.13 x_{2} & -0.87 x_{7}\\
 x_{1}   &  8.02462278997 & +  1.02 x_{11} & +  7.66 x_{4} & +  0.16 x_{15} & -0.66 x_{16} & +  0.87 x_{13} & -7.83 x_{5} & +  0.59 x_{12} & + 22.69 x_{2} & -1.34 x_{7}\\
 x_{17}   &  60.2703878552 & +  8.43 x_{11} & + 71.32 x_{4} & +  2.03 x_{15} & -5.35 x_{16} & +  7.81 x_{13} & -74.60 x_{5} & +  5.06 x_{12} & + 199.67 x_{2} & -14.08 x_{7}\\
\hline
z    &  9.85531796723 & +  1.16 x_{11} & + 16.82 x_{4} & +  0.24 x_{15} & -1.03 x_{16} & +  1.12 x_{13} & -15.43 x_{5} & +  0.61 x_{12} & + 29.25 x_{2} & +  3.62 x_{7}\\
\end{array}\]


 $ x_{2} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  0.0336055305841 & -0.05 x_{11} & -0.31 x_{4} & -0.01 x_{15} & +  0.03 x_{16} & -0.04 x_{13} & +  0.31 x_{5} & -0.02 x_{12} & -0.01 x_{10} & +  0.03 x_{7}\\
 x_{9}   &  2.69530942478 & -0.04 x_{11} & +  0.20 x_{4} & -0.01 x_{15} & -0.01 x_{16} & +  0.04 x_{13} & -0.16 x_{5} & +  0.07 x_{12} & -0.06 x_{10} & -1.05 x_{7}\\
 x_{18}   &  26.0912181536 & -0.04 x_{11} & + 17.87 x_{4} & +  0.29 x_{15} & -0.26 x_{16} & -0.05 x_{13} & -13.44 x_{5} & -0.23 x_{12} & -0.53 x_{10} & + 11.10 x_{7}\\
 x_{6}   &  4.41550537834 & -0.12 x_{11} & +  1.49 x_{4} & +  0.04 x_{15} & -0.11 x_{16} & -0.03 x_{13} & -0.11 x_{5} & +  0.09 x_{12} & -0.13 x_{10} & -0.18 x_{7}\\
 x_{14}   &  7.57005459362 & +  0.27 x_{11} & +  8.81 x_{4} & +  0.09 x_{15} & -0.08 x_{16} & +  0.06 x_{13} & +  1.82 x_{5} & -0.28 x_{12} & +  0.00 x_{10} & -3.12 x_{7}\\
 x_{3}   &  1.77468154798 & -0.06 x_{11} & +  0.64 x_{4} & -0.03 x_{15} & -0.06 x_{16} & +  0.01 x_{13} & -0.07 x_{5} & +  0.02 x_{12} & -0.04 x_{10} & -0.46 x_{7}\\
 x_{8}   &  5.92950051314 & -0.07 x_{11} & +  1.26 x_{4} & +  0.05 x_{15} & -0.02 x_{16} & -0.00 x_{13} & -0.56 x_{5} & +  0.00 x_{12} & -0.11 x_{10} & -0.45 x_{7}\\
 x_{1}   &  8.78714761496 & -0.07 x_{11} & +  0.64 x_{4} & -0.02 x_{15} & -0.08 x_{16} & -0.04 x_{13} & -0.71 x_{5} & +  0.04 x_{12} & -0.16 x_{10} & -0.76 x_{7}\\
 x_{17}   &  66.9804803294 & -1.16 x_{11} & +  9.52 x_{4} & +  0.47 x_{15} & -0.26 x_{16} & -0.19 x_{13} & -11.91 x_{5} & +  0.21 x_{12} & -1.40 x_{10} & -8.94 x_{7}\\
\hline
z    &  10.8381934133 & -0.24 x_{11} & +  7.76 x_{4} & +  0.01 x_{15} & -0.29 x_{16} & -0.05 x_{13} & -6.25 x_{5} & -0.10 x_{12} & -0.20 x_{10} & +  4.38 x_{7}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{2} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  0.10857059858 & -0.16 x_{11} & -3.23 x_{2} & -0.03 x_{15} & +  0.08 x_{16} & -0.13 x_{13} & +  1.01 x_{5} & -0.08 x_{12} & -0.02 x_{10} & +  0.08 x_{7}\\
 x_{9}   &  2.7173862386 & -0.07 x_{11} & -0.66 x_{2} & -0.02 x_{15} & +  0.00 x_{16} & +  0.01 x_{13} & +  0.05 x_{5} & +  0.05 x_{12} & -0.06 x_{10} & -1.04 x_{7}\\
 x_{18}   &  28.0311249649 & -2.81 x_{11} & -57.73 x_{2} & -0.16 x_{15} & +  1.21 x_{16} & -2.36 x_{13} & +  4.68 x_{5} & -1.63 x_{12} & -0.93 x_{10} & + 12.59 x_{7}\\
 x_{6}   &  4.57700205124 & -0.35 x_{11} & -4.81 x_{2} & +  0.01 x_{15} & +  0.01 x_{16} & -0.22 x_{13} & +  1.40 x_{5} & -0.02 x_{12} & -0.17 x_{10} & -0.06 x_{7}\\
 x_{14}   &  8.52640021066 & -1.10 x_{11} & -28.46 x_{2} & -0.14 x_{15} & +  0.65 x_{16} & -1.08 x_{13} & + 10.75 x_{5} & -0.97 x_{12} & -0.20 x_{10} & -2.39 x_{7}\\
 x_{3}   &  1.84384956441 & -0.16 x_{11} & -2.06 x_{2} & -0.05 x_{15} & -0.01 x_{16} & -0.08 x_{13} & +  0.57 x_{5} & -0.03 x_{12} & -0.05 x_{10} & -0.41 x_{7}\\
 x_{8}   &  6.06608386164 & -0.27 x_{11} & -4.06 x_{2} & +  0.01 x_{15} & +  0.08 x_{16} & -0.16 x_{13} & +  0.72 x_{5} & -0.10 x_{12} & -0.14 x_{10} & -0.35 x_{7}\\
 x_{1}   &  8.85642452671 & -0.16 x_{11} & -2.06 x_{2} & -0.03 x_{15} & -0.03 x_{16} & -0.12 x_{13} & -0.06 x_{5} & -0.01 x_{12} & -0.17 x_{10} & -0.70 x_{7}\\
 x_{17}   &  68.0139699743 & -2.64 x_{11} & -30.75 x_{2} & +  0.23 x_{15} & +  0.52 x_{16} & -1.42 x_{13} & -2.25 x_{5} & -0.54 x_{12} & -1.61 x_{10} & -8.15 x_{7}\\
\hline
z    &  11.6811190609 & -1.45 x_{11} & -25.08 x_{2} & -0.19 x_{15} & +  0.35 x_{16} & -1.06 x_{13} & +  1.63 x_{5} & -0.71 x_{12} & -0.38 x_{10} & +  5.02 x_{7}\\
\end{array}\]


 $ x_{5} $ enters and $ x_{17} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  30.7987454532 & -1.34 x_{11} & -17.11 x_{2} & +  0.08 x_{15} & +  0.32 x_{16} & -0.77 x_{13} & -0.45 x_{17} & -0.32 x_{12} & -0.75 x_{10} & -3.59 x_{7}\\
 x_{9}   &  4.25185704711 & -0.13 x_{11} & -1.35 x_{2} & -0.01 x_{15} & +  0.02 x_{16} & -0.02 x_{13} & -0.02 x_{17} & +  0.04 x_{12} & -0.10 x_{10} & -1.22 x_{7}\\
 x_{18}   &  169.727101222 & -8.30 x_{11} & -121.80 x_{2} & +  0.31 x_{15} & +  2.29 x_{16} & -5.33 x_{13} & -2.08 x_{17} & -2.75 x_{12} & -4.29 x_{10} & -4.38 x_{7}\\
 x_{6}   &  46.9294205901 & -1.99 x_{11} & -23.96 x_{2} & +  0.15 x_{15} & +  0.34 x_{16} & -1.10 x_{13} & -0.62 x_{17} & -0.36 x_{12} & -1.17 x_{10} & -5.13 x_{7}\\
 x_{14}   &  333.882514522 & -13.70 x_{11} & -175.57 x_{2} & +  0.94 x_{15} & +  3.14 x_{16} & -7.88 x_{13} & -4.78 x_{17} & -3.54 x_{12} & -7.90 x_{10} & -41.36 x_{7}\\
 x_{3}   &  19.2246769049 & -0.83 x_{11} & -9.92 x_{2} & +  0.01 x_{15} & +  0.12 x_{16} & -0.44 x_{13} & -0.26 x_{17} & -0.17 x_{12} & -0.47 x_{10} & -2.49 x_{7}\\
 x_{8}   &  27.8082084689 & -1.11 x_{11} & -13.90 x_{2} & +  0.09 x_{15} & +  0.25 x_{16} & -0.62 x_{13} & -0.32 x_{17} & -0.27 x_{12} & -0.66 x_{10} & -2.95 x_{7}\\
 x_{1}   &  7.04730996582 & -0.09 x_{11} & -1.24 x_{2} & -0.04 x_{15} & -0.05 x_{16} & -0.09 x_{13} & +  0.03 x_{17} & +  0.00 x_{12} & -0.13 x_{10} & -0.49 x_{7}\\
 x_{5}   &  30.2519397788 & -1.17 x_{11} & -13.68 x_{2} & +  0.10 x_{15} & +  0.23 x_{16} & -0.63 x_{13} & -0.44 x_{17} & -0.24 x_{12} & -0.72 x_{10} & -3.62 x_{7}\\
\hline
z    &  60.8960908821 & -3.35 x_{11} & -47.34 x_{2} & -0.02 x_{15} & +  0.73 x_{16} & -2.09 x_{13} & -0.72 x_{17} & -1.10 x_{12} & -1.54 x_{10} & -0.87 x_{7}\\
\end{array}\]


 $ x_{16} $ enters and $ x_{1} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{4}   &  79.4107234868 & -2.00 x_{11} & -25.69 x_{2} & -0.19 x_{15} & -6.90 x_{1} & -1.37 x_{13} & -0.27 x_{17} & -0.30 x_{12} & -1.65 x_{10} & -6.96 x_{7}\\
 x_{9}   &  6.61833318179 & -0.16 x_{11} & -1.77 x_{2} & -0.02 x_{15} & -0.34 x_{1} & -0.05 x_{13} & -0.01 x_{17} & +  0.04 x_{12} & -0.14 x_{10} & -1.38 x_{7}\\
 x_{18}   &  521.13332121 & -13.01 x_{11} & -183.80 x_{2} & -1.61 x_{15} & -49.86 x_{1} & -9.64 x_{13} & -0.76 x_{17} & -2.59 x_{12} & -10.78 x_{10} & -28.73 x_{7}\\
 x_{6}   &  98.6565433072 & -2.68 x_{11} & -33.08 x_{2} & -0.14 x_{15} & -7.34 x_{1} & -1.74 x_{13} & -0.43 x_{17} & -0.34 x_{12} & -2.13 x_{10} & -8.72 x_{7}\\
 x_{14}   &  815.098889663 & -20.15 x_{11} & -260.48 x_{2} & -1.69 x_{15} & -68.28 x_{1} & -13.78 x_{13} & -2.97 x_{17} & -3.33 x_{12} & -16.79 x_{10} & -74.70 x_{7}\\
 x_{3}   &  37.9189626082 & -1.08 x_{11} & -13.22 x_{2} & -0.09 x_{15} & -2.65 x_{1} & -0.67 x_{13} & -0.18 x_{17} & -0.16 x_{12} & -0.81 x_{10} & -3.79 x_{7}\\
 x_{8}   &  65.6090281777 & -1.62 x_{11} & -20.57 x_{2} & -0.12 x_{15} & -5.36 x_{1} & -1.08 x_{13} & -0.18 x_{17} & -0.25 x_{12} & -1.35 x_{10} & -5.57 x_{7}\\
 x_{16}   &  153.189333091 & -2.05 x_{11} & -27.03 x_{2} & -0.84 x_{15} & -21.74 x_{1} & -1.88 x_{13} & +  0.58 x_{17} & +  0.07 x_{12} & -2.83 x_{10} & -10.61 x_{7}\\
 x_{5}   &  65.7349841886 & -1.65 x_{11} & -19.94 x_{2} & -0.09 x_{15} & -5.03 x_{1} & -1.07 x_{13} & -0.31 x_{17} & -0.22 x_{12} & -1.37 x_{10} & -6.08 x_{7}\\
\hline
z    &  172.596156761 & -4.85 x_{11} & -67.05 x_{2} & -0.63 x_{15} & -15.85 x_{1} & -3.46 x_{13} & -0.30 x_{17} & -1.05 x_{12} & -3.61 x_{10} & -8.61 x_{7}\\
\end{array}\]
Final Dictionary
Solution:  172.596156761
Num Pivots:  12
\end{document}
